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Answer:
(x - 1)² + (y - 4)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (1, 4), so
(x - 1)² + (y - 4)² = r²
The radius is the distance from the centre to a point on the circle
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (4, 8)
r =
= =
=
= 5
Hence
(x - 1)² + (y - 4)² = 5², that is
(x - 1)² + (y - 4)² = 25 ← equation of circle